Download Lecture 7

Lecture 7
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Electric Current
Circuits
Resistance and Ohms law
Temperature variation
Electrical energy
Resistance
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In a conductor, the voltage applied
across the ends of the conductor is
proportional to the current through
the conductor
The constant of proportionality is
the resistance of the conductor
V
R
I
Fig. 17-CO, p.568
Resistance, cont
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Units of resistance are ohms (Ω)
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1Ω=1V/A
Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Georg Simon Ohm
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1787 – 1854
Formulated the
concept of
resistance
Discovered the
proportionality
between current
and voltages
Ohm’s Law
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Experiments show that for many
materials, including most metals, the
resistance remains constant over a wide
range of applied voltages or currents
This statement has become known as
Ohm’s Law
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ΔV = I R
Ohm’s Law is an empirical relationship
that is valid only for certain materials
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Materials that obey Ohm’s Law are said to
be ohmic
Ohm’s Law, cont
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An ohmic device
The resistance is
constant over a wide
range of voltages
The relationship
between current and
voltage is linear
The slope is related
to the resistance
Demo 2
Ohm’s Law, final
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Non-ohmic materials
are those whose
resistance changes
with voltage or
current
The current-voltage
relationship is
nonlinear
A diode is a common
example of a nonohmic device
Resistivity
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The resistance of an ohmic conductor is
proportional to its length, L, and
inversely proportional to its crosssectional area, A
L
R
A
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ρ is the constant of proportionality and is
called the resistivity of the material
Table 17-1, p.576
Temperature Variation of
Resistivity
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For most metals, resistivity
increases with increasing
temperature
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With a higher temperature, the
metal’s constituent atoms vibrate
with increasing amplitude
The electrons find it more difficult to
pass through the atoms
Temperature Variation of
Resistivity, cont
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For most metals, resistivity increases
approximately linearly with temperature
over a limited temperature range
  o [1  (T  To )]
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ρ is the resistivity at some temperature T
ρo is the resistivity at some reference
temperature To
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To is usually taken to be 20° C = 68 ° F
 is the temperature coefficient of resistivity
Temperature Variation of
Resistance
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Since the resistance of a conductor
with uniform cross sectional area is
proportional to the resistivity, you
can find the effect of temperature
on resistance
R  Ro [1 (T  To )]
Superconductors
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A class of materials
and compounds
whose resistances
fall to virtually zero
below a certain
temperature, TC
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TC is called the critical
temperature
The graph is the
same as a normal
metal above TC, but
suddenly drops to
zero at TC
Superconductors, cont
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The value of TC is sensitive to
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Chemical composition
Pressure
Crystalline structure
Once a current is set up in a
superconductor, it persists without
any applied voltage
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Since R = 0
Superconductor Timeline
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1911
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1986
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High temperature superconductivity
discovered by Bednorz and Müller
Superconductivity near 30 K
1987
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Superconductivity discovered by H.
Kamerlingh Onnes
Superconductivity at 96 K and 105 K
Current
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More materials and more applications
Table 17-2, p.579
Superconductor, final
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Good conductors
do not necessarily
exhibit
superconductivity
One application is
superconducting
magnets
Electrical Energy and
Power
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In a circuit, as a charge moves through
the battery, the electrical potential
energy of the system is increased by
ΔQΔV
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The chemical potential energy of the battery
decreases by the same amount
As the charge moves through a resistor,
it loses this potential energy during
collisions with atoms in the resistor
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The temperature of the resistor will increase
Energy Transfer in the
Circuit
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Consider the
circuit shown
Imagine a
quantity of
positive charge,
Q, moving
around the circuit
from point A back
to point A
Energy Transfer in the
Circuit, cont
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Point A is the reference point
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It is grounded and its potential is
taken to be zero
As the charge moves through the
battery from A to B, the potential
energy of the system increases by
QV
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The chemical energy of the battery
decreases by the same amount
Energy Transfer in the
Circuit, final
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As the charge moves through the
resistor, from C to D, it loses energy in
collisions with the atoms of the resistor
The energy is transferred to internal
energy
When the charge returns to A, the net
result is that some chemical energy of
the battery has been delivered to the
resistor and caused its temperature to
rise
Electrical Energy and
Power, cont
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The rate at which the energy is
lost is the power
Q

V  I V
t
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From Ohm’s Law, alternate forms
of power are
V
 I R 
R
2
2
Electrical Energy and
Power, final
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The SI unit of power is Watt (W)
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I must be in Amperes, R in ohms and
V in Volts
The unit of energy used by electric
companies is the kilowatt-hour
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This is defined in terms of the unit of
power and the amount of time it is
supplied
1 kWh = 3.60 x 106 J